The Solution:
Given the fractions below:
[tex]\frac{1}{5}\text{ and }\frac{7}{10}[/tex]We are asked to find the sum of the above two fractions.
[tex]\frac{1}{5}+\frac{7}{10}[/tex]The Lowest Common Multiple (LCM) of 5 and 10 is 10
[tex]\frac{2+7}{10}=\frac{9}{10}[/tex]Thus, the correct answer is
[tex]\frac{9}{10}[/tex]Perpendicular to y=-5x+1 passing through (2,-1)
The equation of the line perpendicular to the given line will be equal to 5y = x - 3.
A line may be defined as a straight figure which is drawn and has no end points. The equation of line in slope intercept form may be written as y = mx + c where m is the slope and c is the y intercept. The equation of line passing through a point (x₁, y₂) will be given as (y - y₁) = m(x - x₁). The slope of line perpendicular to a line having slope m is given by -1/m. The equation of line in the question is y = -5x + 1. The slope of the line is -5. The slope of line perpendicular to this line is 1/5. Equation of line passing through (2, -1) and slope 1/5 is given by
(y + 1) = 1/5(x - 2)
5y + 1 = x -2
5y = x - 3 which is the required equation.
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x^2 - xy = 14
y^2 +xy = 60
The answer is
x = 7, -7, √2, -√2
Add the two equations to get
x2 + y2 = 74
Eliminate y from the first by solving for y and using that result:
(x2 − 14) = x√74 - x2
square both sides, then condense:
x4 − 51x2 + 98 = 0
These ready factors:
(x−7)(x+7)(x−√2)(x+√2)=0
I'll let you handle it from there, but keep in mind that if we square all sides, we might find roots that need to be pulled out afterward.
Therefore,
x = 7, -7, √2, -√2
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Nura made a square poster with a side length of 13 inches. Latrice made a square poster with a side length of 15 inches. Whats the difference in square inches between the area of Latrice's poster and the area of Nura's poster?
The difference between the areas of the posters is 56 in².
QuadrilateralsThere are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a square, all angles are 90° and all sides present the same value.
The area of a square is given by: A= a², where a=the length of the side.
Area of square poster's NuraA=(13 in)²
A= 169 in²
Area of square poster's LatriceA=(15 in)²
A= 225 in²
Therefore, the difference in square inches between the area of Latrice's poster and the area of Nura's poster is 225 - 169=56 in²
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What type of pay is modeled below?
A. Hourly pay with a bonus. B. Hourly pay without a bonus. C. Commission pay D. Piece rate
The type of pay which is modeled in the image attached below is: D) piece rate.
What is a pay?Money or something paid for a purpose and especially as a salary or wage
The types of pay.
In Mathematics, there are four 5) different types of pay and these include:
The different types of compensation include:
Salary.
Hourly Wages.
Sales Commission.
Tips.
Stock Options.
Bonuses.
Incentive Pay.
Other Variable Pay.
Salary
Commission
Bonuses
Piece rate
Method of wage payment that remunerates the employees on the basis of quantity they produced is known as piece rate.
Plucking tea
The number of tee-shirts produced.
Pruning fruit trees
Sorting second-hand clothes (garments)
Hence the graph of a piece rate model is characterized by a straight line with the slope upwards as represented in the image attached.
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(1) PQRS is a rhombus. Prove that APQT = APST by using all four conditions of congruency.
Four conditions of congruency are: SSS, ASA, SAS, RHS
Using SSS congruency,
Side: PS = PQ (by the rule, all sides of rhombus are equal)
Side: ST = TQ (by the rule, diagonals bisect each other)
Side: PT = PT (common)
Therefore, Area(PQT) = Area(PST) by SSS congruency
Using ASA congruency,
Angle: ∠TPS = ∠TPQ (diagonals bisect the angles)
Side: PS = PQ (by the rule, all sides of rhombus are equal)
Angle: ∠PST = ∠PQT (opposite angles are equal, and diagonals bisect the angles)
Therefore, Area(PQT) = Area(PST) by ASA congruency
Using SAS congruency,
Side: ST = TQ (by the rule, diagonals bisect each other)
Angle: ∠PTS = ∠PTQ (by the rule, diagonals bisect each other at 90°)
Side: PT = PT (common)
Therefore, Area(PQT) = Area(PST) by SAS congruency.
Using RHS congruency,
Right angle: ∠PTS = ∠PTQ (diagonals bisect each other at 90°)
Hypotenuse: PS = PQ (all sides of rhombus are equal)
Corresponding Side: ST = TQ (by the rule, diagonals bisect each other)
Therefore, Area(PQT) = Area(PST) by RHS congruency
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He number of nano-related patents that are granted in the us increases by a factor of 1.21.21, point, 2 every year. in 199119911991, there were 606060 nano-related patents. which expression gives the number of patents in 199819981998?
The exponential function y = 60(1.2)7 yields the number of patents in 1998.
The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis. Let y be the number of nanotechnology-related patents issued in the US in year x following 1991.
There were 60 patents on nanotechnology in 1991, and since then there has been a factor of 1.2 increase.
y = 60(1.2)ˣ
y = 60 in 1998 (7 years ago) (1.2)⁷
The exponential function is used to calculate the number of patents in 1998.
y=60(1.2)⁷
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PLEASE HELP!!!!! It’s algebra
Answer:
k=3/10
Step-by-step explanation:
8y=12x+6 >>>>(÷8) both sides
y= (3/2)x+(3/4)
if x=0, y=3/4
4y=k(3x+10) >>> plug in (0, 3/4)
4(3/4)= k(0+10)
3= 10k >>> (÷10) both sides
k=3/10
In the New York State Numbers Lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $750, which is a profit of $749. If you lose, you lose $1. Your probability of winning is 000.1.
Read the question below:
The rule for the function g(x) is g(x) = x - 5 when f(x) = 5 and vertical down to 5 units.
Functions:
Function refers the relationship from a set X to a set Y assigns to each element of X exactly one element of Y
Given,
Let g(x) indicated the transformation of f(x)
Here we need to write the rule for g(x) when f(x) = x, and vertical translation down 5 units.
Here we have the function f(x) = x.
Considering the normal graph, we know that, the graph has four parts.
And each part refers difference sign. That is,
Horizontal left indicates the positive where as the horizontal right refers the negative for x axis.
Similarly, vertical up refers the positive and the vertical down represents the negative.
Here we have the vertical down translation of 5 units which refers the negative 5.
So, the rule of g(x) = x - 5.
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candy and tim share a paper route. it takes candy 50 min to deliver all the papers, and it takes tim 100 min. how long does it take the two when they work together?
It takes a time of 33 mi 33 sec for the two when they work together
Let x be the overall quantity of papers that must be delivered.
Candy can deliver x/50 papers in a minute.
Tim can deliver x/100 papers in a minute.
Tim and Candy took their time gathering all the papers together =x/ (x/50 +x/100)
= x/ (3x/ 100)
=100/ 3 minutes
=33 minutes 33 seconds
When Tim and Candy collaborate, it takes them 33 minutes and 33 seconds to distribute all the papers.
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Answer:
Step-by-step explanation:
It takes a time of 33 min 33 sec.
Let x be the overall quantity of papers that must be delivered.
Candy can deliver x/50 papers in a minute. Tim can deliver x/100 papers in a minute. Tim and Candy took their time gathering all the papers together =x/ (x/50+x/100) = x/(3x/ 100) =100/ 3 minutes =33 minutes 33 seconds
That is When Tim and Candy collaborate, it takes them 33 minutes and 33 seconds to distribute all the papers.
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Write the quadratic function [tex]f(x)=\frac{1}{7} (x^{2} +14x+35)[/tex] in standard form and use it to find the axis of symmetry and the vertex.
Answer:
f(x) = 1/7 * (x + 7)^2 - 2
axis of symmetry: x = -7
vertex: (-7 | -2)
Step-by-step explanation:
f(x) = 1/7 * (x^2 + 14x + 35)
f(x) = 1/7 * (x^2 + 14x) + 5
f(x) = 1/7 * (x^2 + 14x + 7^2 - 7^2) + 5
f(x) = 1/7 * (x^2 + 14x + 7^2 - 49) + 5
f(x) = 1/7 * (x^2 + 14x + 7^2) + 5 - 7
f(x) = 1/7 * (x + 7)^2 + 5 - 7
f(x) = 1/7 * (x + 7)^2 - 2
Below are ten scores for two different students. Students have a choice: they can take the median of their scores as their final grade, or they can take the mean of their scores as a final grade. Scores are rounded to the nearest whole number. For each student tell which option would result in the highest grade.
Student A: 25, 78, 80, 82, 85, 86, 88, 89, 96, 99
Student B: 71, 77, 77, 79, 79, 80, 88, 89, 91, 96
Find the median and mean for both students.
Answer:
Step-by-step explanation:
Student A:
Mean 80.8
Median: 85.5
The Median is a higher score.
Student B:
Mean 82.7
Median: 79.5
Mean is a higher score
Answer:
Student A's median and Student B's mean would result in the highest grade.
Step-by-step explanation:
How to find the mean:
The mean is the average.
Therefore, you must add all numbers listed, then divide the added numbers by the amount of numbers you added together. Lastly, as instructed round to the nearest whole number.
- Student A : Mean = 81
Step 1 : 25+78+80+82+85+86+88+89+96+99 = 808
Step 2: 808 ÷ 10 = 80.8
Step 3: 80.8 ---> 81
- Student B: Mean = 83
Step 1: 71+77+77+79+79+80+88+89+91+96 = 827
Step 2: 827 ÷ 10 = 82.7
Step 3: 82.7 ---> 83
How to find the median:
The median is the middle number in a sorted list of numbers.
Therefore, you list all of the numbers from least to greatest. Then, you get rid of a number from each side until you finally get to the center number. If there are two numbers left in the center you then find the mean(average) of those numbers.
- Student A: Median = 86
Step 1: Knock off a number from each side until you reach the center number(s)
25, 78, 80, 82, 85, 86, 88, 89, 96, 99 ---> 85, 86
Step 2: Find the mean(average) of the two central numbers
85 + 86 = 171 ---> 171 ÷ 2 = 85.5
Step 3: Round your answer
85.5 ---> 86
- Student B: Median = 80
Step1: Knock off a number from each side until you reach the center number(s)
71, 77, 77, 79, 79, 80, 88, 89, 91, 96 ---> 79, 80
Step 2: Find the mean(average) of the two central numbers
79 + 80 ---> 159 ÷ 2 = 79.5
Step 3: Round your answer
79.5 ---> 80
A painting in the shape of a rectangle has side lengths of 30 inches and
21 inches. You buy a print of the painting with side lengths of 10 inches and
7 inches. Is the print similar to the original painting? Explain your reasoning
Answer:
Yes! The painting is similar.
Step-by-step explanation:
The sides of the original painting are 30 and 21. If you divide this by 3, it equals 10 and 7 which are the sides of the print. This means that the ratio is right so the paintings are similar.
Write an equation that represents the line.
Use exact numbers.
Answer: y=3/4x-4.5
Step-by-step explanation: Looking at the two points on the line, it goes up 3 times and right 4 times, making it 3/4x. To find the y-intercept, you look where the line intersects the y-axis, and it intersects at y=-4.5.
three friends ate at a restaurant. they ordered nachos for $19.95 and jalapeno poppers. each friend paid $9.73, not including sales tax or tip, which was one third of the total. determine the cost of the jalapeno poppers. $6.65 $9.24 $18.48 $29.19
The cost of the jalapeno poppers was $9.24 if each friend paid $9.73.
The cost of the jalapeno poppers can be determined by using multiplication followed by subtraction.
First, we determine the total amount paid by the three friends;
If each friend paid $9.73, then;
Total amount = 9.73 × 3
Total amount = $29.19
Now to find the cost of jalapeno poppers, we subtract the cost of nachos from the total amount paid by the three friends;
cost of jalapeno poppers = total amount - cost of nachos
cost of jalapeno poppers = 29.19 - 19.95
cost of jalapeno poppers = $9.24
Therefore, the cost of jalapeno poppers is calculated to be $9.24.
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Help please:):)
Create a table of data for two different linear functions. The table should use that same values of x for both functions. Based on your table, will the graph of these two functions intersect? Explain your answer
Graph of two linear functions y=2x+7 and y=-x+4 will intersect at (1,5)
What do you means by linear function?
A linear function produces a straight line in the algebraic coordinate plane. It often takes the form of a polynomial function with a maximum degree of 1 or 0.
Calculus and linear algebra are also used to express the linear functions.
The primary distinction can be found in the function notation.
An ordered pair stated in function notation must be understood.
Below is a data table for two distinct linear functions with the identical x values for both functions.
x | y=2x+7 y=-x+4 -3 | 2(-3)+7=-6+7=1| -(-3)+4=3+4=7 -2 | 2(-2)+7=-4+7=3|-(-2)+4=2+4=6 -1 | 2(-1)+7=-2+7=5|-(-1)+4=1+4=5 0 | 2(0)+7=0+7=7 |-(0)+4=0+4=4 1 | 2(1)+7=2+7+9 |-(1)+4=-1+4=3 2 | 2(2)+7=4+7=11|-(2)+4=-2+4=2 3 | 2(3)+7=6+7=13|-(3)+4=-3+4=1
The table demonstrates that the function y = 2x + 7 and the function y = -x + 4 both have values of 5 for x = -1.
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Please help me. I tried every answer possible. Due today. I’ll give brainliest too
Can you please help me?
Thank you
Answer:
-2/5
Step-by-step explanation:
m = (10 - 8)/(31 - 36) = 2/(-5) = -2/5
Jim and Maureen are training for a marathon. Jim runs 6 kilometers at a time while Maureen prefers to run in blocks of 3 kilometers. At the end of the month, they realize that they have run the same total number of kilometers. What is the smallest number of kilometers that each must run?
The smallest number of kilometers that each must run is 6 kilometers.
What will be the least common multiple?From the information, Jim runs 6 kilometers at a time while Maureen prefers to run in blocks of 3 kilometers and at the end of the month, they realize that they have run the same total number of kilometers.
It should be noted that the question simony had to do with finding the least common multiple. This will be:
Multiple of 3 = 3, 6, 9, 12
Multiple of 6 = 6, 12
The least common multiple is 6.
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Evaluate. Write your answer as a whole number or as a simplified fraction.
please help meee
xddd
Answer:
I'm thinking it's 22, but I could be wrong.
Step-by-step explanation:
Find the derivative, if it exists, of the function at the specified point.() = ^2 − 4 + 3 at = 1
Find the derivate of the expression using the general procedure to find the derivative of a polynomial function. To do it, multiply the term times the exponent of the variable and raise the variable to the original exponent minus 1:
[tex]\begin{gathered} f(x)=x^2-4x+3 \\ f^{\prime}(x)=2x^{2-1}-4x^{1-1}-0\cdot3 \\ f^{\prime}(x)=2x-4 \end{gathered}[/tex]Now that we have the expression for the derivative of the function, evaluate it at the value of x that is in the question statement, which is 1:
[tex]f^{\prime}(1)=2(1)-4=2-4=-2[/tex]The derivative of the function is -2 at x=1.
Leo has three times as many colored marbles as he has clear-glass marbles. In total, he has 60 marbles. How many clear-glass marbles does he have?
Answer:
15
Step-by-step explanation:
Supposing:
Coloured marbles = x
Glass marbles = y
According to Question
x = 3y
As,
x + y = 60
3y + y = 60 (putting value of x = 3y)
4y = 60
y = 60/4
y = 15
Hence, Leo has 15 Clear-glass marbles
[(4•(-2)+(-3)]•(4-2-(-3)
Step-by-step explanation:
hope it helps you
thank you
While exercising George walked 1/2 of a mile in 1/3 of an hour. At this rate, how far will he have travelled after an hour?
Answer: 1 1/2 in a hour
Step-by-step explanation:
1/2 every 1/3 so if we add one more half it is 1 and 2/3 the last one is 1 1/2 is 1 full hour.
1 In a recipe, for every cup sugar, 3 cup flour is needed. How many cups of sugar 4 are needed for 1 cup of flour? Write your answers in the blanks. 13334 || = 1/ 3 IL *
I need first 2 blanks then 2 more blanks flilled in.
In the given recipe, 1/3 cup of sugar is needed for 1 cup of flour.
What do you mean by recipe?
A recipe is a set of instructions for preparing a dish or dessert, such as your mother's chocolate chip cookie recipe, which has won numerous awards.
The phrase "recipe" is most frequently used while discussing cookery. It covers both the steps to prepare it as well as a list of the ingredients you'll need. Recipes can be found in cookbooks, newspapers, periodicals, websites, publications, and even passed down via families. A recipe isn't just for cooking; it may also be a formula: the formula for success is a combination of diligence, timing, and a little luck.
As given in the question, In the recipe
For every cup of sugar, 3 cups of flour is needed. we can write it as:
1 cup of sugar = 3 cups of flour
we need to find how many cups of sugar needed for 1 cup of flour.
So, dividing the above equation with 3.
1/3 cups of sugar = 1 cups of flour.
Therefore, In the given recipe, 1/3 cups of sugar is required for 1 cup of flour.
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Complete the following statement. Use the integers that are closest to the number in the middle.
? < 90 < ?
The integers that are closest to the number in the middle will be 89 < 90 < 91.
What is an integer?It should be noted that an integer simply means a whole number that can be positive, negative, or zero.
It should be noted that on this case, we have to look for the numbers that are closest to 90 one has to be less than 90 and the other one should be greater than it.
Therefore, the numbers that fits the information will be 89 and 91.
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An art teacher found that in a bin of markers, of the caps had been left off the markers. of these markers, of them were dried up. use the model to find what fraction of the markers had the lids left off and were dried up.
Answer:
there is no model linked
Step-by-step explanation:
(−20/35)÷12/20 What is the quotient
Answer:
-1/420
Step-by-step explanation:
-4/7/12/20
= -1/21/20
= -1/420
SAT QUESTION HELLP ME
Answer:
22.5
Step-by-step explanation:
we can use the ratios to turn x+y+z=180 to x+4x+3x= 180
then solve for 180
x = 22.5
Answer: D.) 22.5°
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